English

The Length of the Perpendicular Drawn from the Point P(A, B, C) from Z-axis is - Mathematics

Advertisements
Advertisements

Question

The length of the perpendicular drawn from the point P(a, b, c) from z-axis is 

Options

  • \[\sqrt{a^2 + b^2}\] 

  • \[\sqrt{b^2 + c^2}\] 

  • \[\sqrt{a^2 + c^2}\]

  •  \[\sqrt{a^2 + b^2 + c^2}\]

MCQ
Advertisements

Solution

The length of the perpendicular drawn from the point P(x, y, z) from z-axis is given by \[\sqrt{y^2 + x^2}\] Thus, the length of the perpendicular drawn from the point P(a, b, c) from z-axis is \[\sqrt{a^2 + b^2}\] 

Hence, the correct answer is option (a)

shaalaa.com
  Is there an error in this question or solution?
Chapter 28: Introduction to three dimensional coordinate geometry - Exercise 28.5 [Page 23]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 28 Introduction to three dimensional coordinate geometry
Exercise 28.5 | Q 15 | Page 23

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Coordinate planes divide the space into ______ octants.


Name the octants in which the following points lie: 

(4, –3, 5)


Name the octants in which the following points lie:

 (2, –5, –7) 


Find the image  of: 

 (–4, 0, 0) in the xy-plane. 


The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.


Determine the points in zx-plane are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1). 


Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.


Find the locus of the points which are equidistant from the points (1, 2, 3) and (3, 2, –1).


Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.


Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.


Find the ratio in which the sphere x2 + y2 z2 = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).


Show that the plane ax + by cz + d = 0 divides the line joining the points (x1y1z1) and (x2y2z2) in the ratio \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]


Write the length of the perpendicular drawn from the point P(3, 5, 12) on x-axis.


Find the point on y-axis which is at a distance of  \[\sqrt{10}\] units from the point (1, 2, 3).


Find the point on x-axis which is equidistant from the points A (3, 2, 2) and B (5, 5, 4).


XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


Find the image of the point having position vector `hati + 3hatj + 4hatk` in the plane `hatr * (2hati - hatj + hatk)` + 3 = 0.


The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by ______.


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).


If a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2


Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a′, b′, c′, respectively, from the origin, prove that

`1/a^2 + 1/b^2 + 1/c^2 = 1/(a"'"^2) + 1/(b"'"^2) + 1/(c"'"^2)`


Find the foot of perpendicular from the point (2,3,–8) to the line `(4 - x)/2 = y/6 = (1 - z)/3`. Also, find the perpendicular distance from the given point to the line.


Find the equation of the plane through the points (2, 1, –1) and (–1, 3, 4), and perpendicular to the plane x – 2y + 4z = 10.


Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0.


If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.


The sine of the angle between the straight line `(x - 2)/3 = (y - 3)/4 = (z - 4)/5` and the plane 2x – 2y + z = 5 is ______.


The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.


The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.


The cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.


The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.


The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×